Leonhard Euler (13937-1)

Leonhard
Euler's father was Paul Euler. Paul Euler had studied theology at the
University of Basel and had attended Jacob Bernoulli's lectures
there. In fact Paul Euler and Johann Bernoulli had both lived in
Jacob Bernoulli's house while undergraduates at Basel. Paul Euler
became a Protestant minister and married Margaret Brucker, the
daughter of another Protestant minister. Their son Leonhard Euler was
born in Basel, but the family moved to Riehen when he was one year
old and it was in Riehen, not far from Basel, that Leonard was
brought up. Paul Euler had, as we have mentioned, some mathematical
training and he was able to teach his son elementary mathematics
along with other subjects.

Leonhard
was sent to school in Basel and during this time he lived with his
grandmother on his mother's side. This school was a rather poor one,
by all accounts, and Euler learnt no mathematics at all from the
school. However his interest in mathematics had certainly been
sparked by his father's teaching, and he read mathematics texts on
his own and took some private lessons. Euler's father wanted his son
to follow him into the church and sent him to the University of Basel
to prepare for the ministry. He entered the University in 1720, at
the age of 14, first to obtain a general education before going on to
more advanced studies. Johann Bernoulli soon discovered Euler's great
potential for mathematics in private tuition that Euler himself
engineered. Euler's own account given in his unpublished
autobiographical writings, see, is as follows:-

...
I soon found an opportunity to be introduced to a famous professor
Johann Bernoulli. ... True, he was very busy and so refused flatly to
give me private lessons; but he gave me much more valuable advice to
start reading more difficult mathematical books on my own and to
study them as diligently as I could; if I came across some obstacle
or difficulty, I was given permission to visit him freely every
Sunday afternoon and he kindly explained to me everything I could not
understand ...

In
1723 Euler completed his Master's degree in philosophy having
compared and contrasted the philosophical ideas of Descartes and
Newton. He began his study of theology in the autumn of 1723,
following his father's wishes, but, although he was to be a devout
Christian all his life, he could not find the enthusiasm for the
study of theology, Greek and Hebrew that he found in mathematics.
Euler obtained his father's consent to change to mathematics after
Johann Bernoulli had used his persuasion. The fact that Euler's
father had been a friend of Johann Bernoulli's in their undergraduate
days undoubtedly made the task of persuasion much easier.

Euler
completed his studies at the University of Basel in 1726. He had
studied many mathematical works during his time in Basel, and
Calinger has reconstructed many of the works that Euler read with the
advice of Johann Bernoulli. They include works by Varignon,
Descartes, Newton, Galileo, von Schooten, Jacob Bernoulli, Hermann,
Taylor and Wallis. By 1726 Euler had already a paper in print, a
short article on isochronous curves in a resisting medium. In 1727 he
published another article on reciprocal trajectories and submitted an
entry for the 1727 Grand Prize of the Paris Academy on the best
arrangement of masts on a ship.

The
Prize of 1727 went to Bouguer, an expert on mathematics relating to
ships, but Euler's essay won him second place which was a fine
achievement for the young graduate. However, Euler now had to find
himself an academic appointment and when Nicolaus(II) Bernoulli died
in St Petersburg in July 1726 creating a vacancy there, Euler was
offered the post which would involve him in teaching applications of
mathematics and mechanics to physiology. He accepted the post in
November 1726 but stated that he did not want to travel to Russia
until the spring of the following year. He had two reasons to delay.
He wanted time to study the topics relating to his new post but also
he had a chance of a post at the University of Basel since the
professor of physics there had died. Euler wrote an article on
acoustics, which went on to become a classic, in his bid for
selection to the post but he was nor chosen to go forward to the
stage where lots were drawn to make the final decision on who would
fill the chair. Almost certainly his youth (he was 19 at the time)
was against him. However Calinger suggests:-

This
decision ultimately benefited Euler, because it forced him to move
from a small republic into a setting more adequate for his brilliant
research and technological work.

As
soon as he knew he would not be appointed to the chair of physics,
Euler left Basel on 5 April 1727. He travelled down the Rhine by
boat, crossed the German states by post wagon, then by boat from
Lübeck arriving in St Petersburg on 17 May 1727. He had joined
the St. Petersburg Academy of Science two years after it had been
founded by Catherine I the wife of Peter the Great. Through the
requests of Daniel Bernoulli and Jakob Hermann, Euler was appointed
to the mathematical-physical division of the Academy rather than to
the physiology post he had originally been offered. At St Petersburg
Euler had many colleagues who would provide an exceptional
environment for him:-

Nowhere
else could he have been surrounded by such a group of eminent
scientists, including the analyst, geometer Jakob Hermann, a
relative; Daniel Bernoulli, with whom Euler was connected not only by
personal friendship but also by common interests in the field of
applied mathematics; the versatile scholar Christian Goldbach, with
whom Euler discussed numerous problems of analysis and the theory of
numbers; F Maier, working in trigonometry; and the astronomer and
geographer J-N Delisle.

Euler
served as a medical lieutenant in the Russian navy from 1727 to 1730.
In St Petersburg he lived with Daniel Bernoulli who, already unhappy
in Russia, had requested that Euler bring him tea, coffee, brandy and
other delicacies from Switzerland. Euler became professor of physics
at the academy in 1730 and, since this allowed him to became a full
member of the Academy, he was able to give up his Russian navy post.

Daniel
Bernoulli held the senior chair in mathematics at the Academy but
when he left St Petersburg to return to Basel in 1733 it was Euler
who was appointed to this senior chair of mathematics. The financial
improvement which came from this appointment allowed Euler to marry
which he did on 7 January 1734, marrying Katharina Gsell, the
daughter of a painter from the St Petersburg Gymnasium. Katharina,
like Euler, was from a Swiss family. They had 13 children altogether
although only five survived their infancy. Euler claimed that he made
some of his greatest mathematical discoveries while holding a baby in
his arms with other children playing round his feet.

We
will examine Euler's mathematical achievements later in this article
but at this stage it is worth summarising Euler's work in this period
of his career. This is done in [24] as follows:-

...
after 1730 he carried out state projects dealing with cartography,
science education, magnetism, fire engines, machines, and ship
building. ... The core of his research program was now set in place:
number theory; infinitary analysis including its emerging branches,
differential equations and the calculus of variations; and rational
mechanics. He viewed these three fields as intimately interconnected.
Studies of number theory were vital to the foundations of calculus,
and special functions and differential equations were essential to
rational mechanics, which supplied concrete problems.

The
publication of many articles and his book Mechanica (1736-37), which
extensively presented Newtonian dynamics in the form of mathematical
analysis for the first time, started Euler on the way to major
mathematical work.

Euler's
health problems began in 1735 when he had a severe fever and almost
lost his life. However, he kept this news from his parents and
members of the Bernoulli family back in Basel until he had recovered.
In his autobiographical writings Euler says that his eyesight
problems began in 1738 with overstrain due to his cartographic work
and that by 1740 he had :-

...
lost an eye and [the other] currently may be in the same danger.

However,
Calinger in [24] argues that Euler's eyesight problems almost
certainly started earlier and that the severe fever of 1735 was a
symptom of the eyestrain. He also argues that a portrait of Euler
from 1753 suggests that by that stage the sight of his left eye was
still good while that of his right eye was poor but not completely
blind. Calinger suggests that Euler's left eye became blind from a
later cataract rather than eyestrain.

By
1740 Euler had a very high reputation, having won the Grand Prize of
the Paris Academy in 1738 and 1740. On both occasions he shared the
first prize with others. Euler's reputation was to bring an offer to
go to Berlin, but at first he preferred to remain in St Petersburg.
However political turmoil in Russia made the position of foreigners
particularly difficult and contributed to Euler changing his mind.
Accepting an improved offer Euler, at the invitation of Frederick the
Great, went to Berlin where an Academy of Science was planned to
replace the Society of Sciences. He left St Petersburg on 19 June
1741, arriving in Berlin on 25 July. In a letter to a friend Euler
wrote:-

I
can do just what I wish [in my research] ... The king calls me his
professor, and I think I am the happiest man in the world.

Even
while in Berlin Euler continued to receive part of his salary from
Russia. For this remuneration he bought books and instruments for the
St Petersburg Academy, he continued to write scientific reports for
them, and he educated young Russians.